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Futwora™ Pro Family Aa1 Aa1 Aa1 Think Work Observe, Type Dept. Futwora™ Pro Type Specimen 32 pts Regular Regular Oblique Medium Medium Oblique Bold Bold Oblique 13 pts 48 pts a a a a a a Futwora™ Pro Type Specimen Page 1 / 21 © 2017 Two Type Dept.

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Page 1: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

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32 pts

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Page 2: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

8 pts Family Name: Futwora™ ProEncoding: Latin ExtendedFile Format: OpenType CFFDesigner: Piero Di Biase (2010–2017)at Think Work Observe Type Dept. Release: 2011/2017Version: 4.0Enquiries: [email protected]

About Futwora™ Pro Futwora Pro is a geometric sans–serif typeface that took inspiration from different styles. Started as an homage to Paul Renner’s masterpiece “Futura”, has been also influenced by the work of designer such Jakob Erbar and Herb Lubalin. Developed with plenty of glyphs and alternative sets it supports Standard Western and Latin Extended characters. Futwora Pro has been widely used by designers all over the world, for magazines, music labels, packaging, posters.

Styles: Regular, Oblique, Medium, Medium Oblique, Bold, Bold Oblique.

Features: 6 stylistic alternates sets, contextual alternates (left and right arrows, multiply), latin extended (base, Western, Central & South Western Europe, Afrikaans), localized forms (Catalan, Dutch, Moldavian, Romanian, Turkish), old style figures, standard ligatures.

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Futwora RegularFutwora Reg ObliqueFutwora MediumFutwora Md ObliqueFutwora BoldFutwora Bd Oblique

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Page 3: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

18 pts Two Type Dept. Futwora™ ProType Specimen

Character Set

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Futwora™ Pro Type Specimen Page 3 / 21 © 2017 Two Type Dept.

Page 4: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

8 pts Supported languagesAfrikaans, Albanian, Asu, Basque, Bemba, Bena, Bosnian, Catalan, Chiga, Congo Swahili, Cornish, Croatian, Czech, Danish, Dutch, Embu, English, Esperanto, Estonian, Faroese, Filipino, Finnish, French, Galician, Ganda, German, Gusii, Hungarian, Icelandic, Indonesian, Irish, Italian, Jola-Fonyi, Kabuverdianu, Kalaallisut, Kalenjin, Kamba, Kikuyu, Kinyarwanda, Latvian, Lithuanian, Luo, Luyia, Machame,

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Page 5: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

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OpenType®OpenType® is a cross-platform font file format developed jointly by Adobe and Microsoft. The two main benefits of the OpenType format are its cross-platform compatibility (the same font file works on Macintosh and Windows computers), and its ability to support widely expanded character sets and layout features, which provide richer linguistic

support and advanced typographic control. OpenType fonts containing PostScript data have an .otf suffix in the font file name, while TrueType-based OpenType fonts have a .ttf file name suffix. OpenType fonts can include an expanded character set and layout features, providing broader linguistic support and more precise typographic control. Feature-rich

OpenType fonts can be distinguished by the word "Pro," which is part of the font name and appears in application font menus. OpenType fonts can be installed and used alongside PostScript Type 1 and TrueType fonts.

Source: http://www.adobe.com/products/type/opentype.html

8 pts

8 pts

24 pts

Futwora™ Pro Type Specimen Page 5 / 21 © 2017 Two Type Dept.

Page 6: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

8 pts

8 pts

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OpenType Features: Automatic Fractions, Ligatures, Old Style Figures, Superscripts and Subscripts

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Futwora™ Pro Type Specimen Page 6 / 21 © 2017 Two Type Dept.

Page 7: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

Two Type Dept. Futwora™ ProType Specimen

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Page 8: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

Regular

Qa1Oblique

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Isaac Newton,Bernhard

Riemann, Kurt Gödel, BlaisePascal, PierreDe Fermat,

and Leonardo Fibonacci!

Mathematics arises from many different kinds of problems. At first these were found in com-merce, land measurement, archi-tecture and later astronomy; today, all sciences suggest problems studied by mathematicians, and many problems arise within mathe-matics itself. For example, the

physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-de-veloping scientific theory which attempts to unify the four funda-mental forces of nature, continues

to inspire new mathematics. Some mathematics is relevant only in the area that inspired it, and is applied to solve further problems in that area.

Source: https://en.wikipe-dia.org/wiki/Mathematics

Futwora™ Pro Type Specimen Page 8 / 21 © 2017 Two Type Dept.

Page 9: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

15 pts

13 pts

Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive charac-ter of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

Aristotle defined mathematics as "the science of quanti-ty", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathemat-ics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathe-matics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among pro-fessionals. There is not even consensus on whether mathe-matics is an art or a science.Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quanti-ty and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the defini-tion of mathematics prevails, even among professionals. There is not even consen-sus on whether mathematics is an art or a science.

Die Entwicklung der ersten Hälfte des 20. Jahrhunderts stand unter dem Einfluss von David Hilberts Liste von 23 mathematischen Problemen. Eines der Probleme war der Versuch einer vollständigen Axiomatisierung der Mathe-matik; gleichzeitig gab es starke Bemühungen zur

Abstraktion, also des Versuches, Objekte auf ihre wesentlichen Eigenschaften zu reduzieren. So entwick-elte Emmy Noether die Grundlagen der modernen Algebra, Felix Hausdorff die allgemeine Topologie als die Untersuchung topologischer Räume, Stefan Banach den

wohl wichtigsten Begriff der Funktionalanalysis, den nach ihm benannten Banachraum. Eine noch höhere Abstraktionsebene, einen gemeinsamen Rahmen für die Betrachtung ähnlich-er Konstruktionen aus verschiedenen Bereichen der Mathematik, schuf

schließlich die Einführung der Kategorientheorie durch Samuel Eilenberg und Saunders Mac Lane.

Source: https://de.wikipe-dia.org/wiki/Mathematics

8 pts

9 pts

Futwora™ Pro Type Specimen Page 9 / 21 © 2017 Two Type Dept.

Page 10: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

Isaac Newton,Bernhard

Riemann, Kurt Gödel, BlaisePascal, PierreDe Fermat,

and Leonardo Fibonacci!

Mathematics arises from many different kinds of problems. At first these were found in com-merce, land measurement, archi-tecture and later astronomy; today, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example,

the physicist Richard Feynman invented the path integral formula-tion of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature,

continues to inspire new mathe-matics. Some mathematics is relevant only in the area that inspired it, and is applied to solve further problems in that area.

Source: https://en.wikipe-dia.org/wiki/Mathematics

8 pts

8 pts

280 pts

8 pts

280 pts

Futwora™ Pro Type Specimen Page 10 / 21 © 2017 Two Type Dept.

Page 11: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

15 pts

13 pts

Die Entwicklung der ersten Hälfte des 20. Jahrhunderts stand unter dem Einfluss von David Hilberts Liste von 23 mathematischen Problemen. Eines der Probleme war der Versuch einer vollständigen Axiomatisierung der Mathe-matik; gleichzeitig gab es starke Bemühungen zur

Abstraktion, also des Versuches, Objekte auf ihre wesentlichen Eigenschaften zu reduzieren. So entwick-elte Emmy Noether die Grundlagen der modernen Algebra, Felix Hausdorff die allgemeine Topologie als die Untersuchung topologischer Räume, Stefan Banach den

wohl wichtigsten Begriff der Funktionalanalysis, den nach ihm benannten Banachraum. Eine noch höhere Abstraktionsebene, einen gemeinsamen Rahmen für die Betrachtung ähnlich-er Konstruktionen aus verschiedenen Bereichen der Mathematik, schuf

schließlich die Einführung der Kategorientheorie durch Samuel Eilenberg und Saunders Mac Lane.

Source: https://de.wikipe-dia.org/wiki/Mathematics

8 pts

9 pts

Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive charac-ter of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

Aristotle defined mathematics as "the science of quanti-ty", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathemat-ics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathe-matics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among pro-fessionals. There is not even consensus on whether mathe-matics is an art or a science.Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quanti-ty and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the defini-tion of mathematics prevails, even among professionals. There is not even consen-sus on whether mathematics is an art or a science.

Futwora™ Pro Type Specimen Page 11 / 21 © 2017 Two Type Dept.

Page 12: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

Two Type Dept. Futwora™ ProType Specimen

Medium, Medium Oblique

Medium

Rb2Medium Oblique

Rb2

8 pts

240 pts

8 pts

240 pts

18 pts

Futwora™ Pro Type Specimen Page 12 / 21 © 2017 Two Type Dept.

Page 13: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

9 pts

64 pts

Isaac Newton,Bernhard

Riemann, Kurt Gödel, BlaisePascal, PierreDe Fermat,

and Leonardo Fibonacci!

Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy; today, all sciences suggest prob-lems studied by mathematicians, and many problems arise within mathematics itself. For example,

the physicist Richard Feynman invented the path integral formu-lation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature,

continues to inspire new mathe-matics. Some mathematics is relevant only in the area that inspired it, and is applied to solve further problems in that area.

Source: https://en.wikipe-dia.org/wiki/Mathematics

Futwora™ Pro Type Specimen Page 13 / 21 © 2017 Two Type Dept.

Page 14: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

15 pts

13 pts

Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive charac-ter of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

Aristotle defined mathematics as "the science of quanti-ty", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathe-matics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these defi-nitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the defini-tion of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

Die Entwicklung der ersten Hälfte des 20. Jahrhunderts stand unter dem Einfluss von David Hilberts Liste von 23 mathematischen Problemen. Eines der Probleme war der Versuch einer vollständigen Axiomatisierung der Mathematik; gleichzeitig gab es starke Bemühungen

zur Abstraktion, also des Versuches, Objekte auf ihre wesentlichen Eigenschaften zu reduzieren. So entwick-elte Emmy Noether die Grundlagen der modernen Algebra, Felix Hausdorff die allgemeine Topologie als die Untersuchung topologischer Räume, Stefan Banach den

wohl wichtigsten Begriff der Funktionalanalysis, den nach ihm benannten Banachraum. Eine noch höhere Abstraktionsebene, einen gemeinsamen Rahmen für die Betrachtung ähnlich-er Konstruktionen aus verschiedenen Bereichen der Mathematik, schuf

schließlich die Einführung der Kategorientheorie durch Samuel Eilenberg und Saunders Mac Lane.

Source: https://de.wikipe-dia.org/wiki/Mathematics

8 pts

9 pts

Futwora™ Pro Type Specimen Page 14 / 21 © 2017 Two Type Dept.

Page 15: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

9 pts

64 pts

Isaac Newton,Bernhard

Riemann, Kurt Gödel, BlaisePascal, Pierre

De Fermat,and Leonardo

Fibonacci!

Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy; today, all sciences suggest prob-lems studied by mathematicians, and many problems arise within mathematics itself. For example,

the physicist Richard Feynman invented the path integral formu-lation of quantum mechanics using a combination of mathemat-ical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature,

continues to inspire new mathe-matics. Some mathematics is relevant only in the area that inspired it, and is applied to solve further problems in that area.

Source: https://en.wikipe-dia.org/wiki/Mathematics

Futwora™ Pro Type Specimen Page 15 / 21 © 2017 Two Type Dept.

Page 16: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

15 pts

13 pts

Die Entwicklung der ersten Hälfte des 20. Jahrhunderts stand unter dem Einfluss von David Hilberts Liste von 23 mathematischen Problemen. Eines der Probleme war der Versuch einer vollständigen Axiomatisierung der Mathematik; gleichzeitig gab es starke Bemühungen

zur Abstraktion, also des Versuches, Objekte auf ihre wesentlichen Eigenschaften zu reduzieren. So entwick-elte Emmy Noether die Grundlagen der modernen Algebra, Felix Hausdorff die allgemeine Topologie als die Untersuchung topologischer Räume, Stefan Banach den

wohl wichtigsten Begriff der Funktionalanalysis, den nach ihm benannten Banachraum. Eine noch höhere Abstraktionsebene, einen gemeinsamen Rahmen für die Betrachtung ähnlicher Konstruktionen aus verschiedenen Bere-ichen

der Mathematik, schuf schließlich die Einführung der Kategorientheorie durch Samuel Eilenberg und Saunders Mac Lane.

Source: https://de.wikipe-dia.org/wiki/Mathematics

8 pts

9 pts

Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive char-acter of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

Aristotle defined mathematics as "the science of quanti-ty", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathe-matics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these defi-nitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the defini-tion of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

Futwora™ Pro Type Specimen Page 16 / 21 © 2017 Two Type Dept.

Page 17: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

Two Type Dept. Futwora™ ProType Specimen

Bold, Bold Oblique

18 pts

Bold

Gk7Bold Oblique

Gk7

8 pts

240 pts

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240 pts

Futwora™ Pro Type Specimen Page 17 / 21 © 2017 Two Type Dept.

Page 18: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

Bold

Gk7Bold Oblique

Gk7

9 pts

64 pts

Isaac Newton,Bernhard

Riemann, Kurt Gödel, BlaisePascal, Pierre

De Fermat,and Leonardo

Fibonacci!

Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy; today, all sciences suggest prob-lems studied by mathematicians, and many problems arise within mathematics itself. For example,

the physicist Richard Feynman invented the path integral formu-lation of quantum mechanics using a combination of mathemat-ical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature,

continues to inspire new mathe-matics. Some mathematics is relevant only in the area that inspired it, and is applied to solve further problems in that area.

Source: https://en.wikipe-dia.org/wiki/Mathematics

Futwora™ Pro Type Specimen Page 18 / 21 © 2017 Two Type Dept.

Page 19: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

15 pts

13 pts

Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive char-acter of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

Aristotle defined mathematics as "the science of quanti-ty", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathe-matics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

Die Entwicklung der ersten Hälfte des 20. Jahrhunderts stand unter dem Einfluss von David Hilberts Liste von 23 mathematischen Proble-men. Eines der Probleme war der Versuch einer vollständigen Axiomatisi-erung der Mathematik; gleichzeitig gab es starke

Bemühungen zur Abstrak-tion, also des Versuches, Objekte auf ihre wesentli-chen Eigenschaften zu reduzieren. So entwickelte Emmy Noether die Grundla-gen der modernen Algebra, Felix Hausdorff die allge-meine Topologie als die Untersuchung topologischer

Räume, Stefan Banach den wohl wichtigsten Begriff der Funktionalanalysis, den nach ihm benannten Banachraum. Eine noch höhere Abstraktionsebene, einen gemeinsamen Rahmen für die Betrachtung ähnlicher Konstruktionen aus verschiedenen Bere-

ichen der Mathematik, schuf schließlich die Einführung der Kategorien-theorie durch Samuel Eilenberg und Saunders Mac Lane.

Source: https://de.wikipe-dia.org/wiki/Mathematics

8 pts

9 pts

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Page 20: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

9 pts

64 pts

Isaac Newton,Bernhard

Riemann, Kurt Gödel, BlaisePascal, Pierre

De Fermat,and Leonardo

Fibonacci!

Mathematics arises from many different kinds of problems. At first these were found in commerce, land measurement, architecture and later astronomy; today, all sciences suggest prob-lems studied by mathematicians, and many problems arise within mathematics itself. For example,

the physicist Richard Feynman invented the path integral formu-lation of quantum mechanics using a combination of mathe-matical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature,

continues to inspire new mathe-matics. Some mathematics is relevant only in the area that inspired it, and is applied to solve further problems in that area.

Source: https://en.wikipe-dia.org/wiki/Mathematics

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Page 21: Futwora™ Pro Family 48 pts Aa1 13 pts Bold Oblique Medium ...physicist Richard Feynman invent-ed the path integral formulation of quantum mechanics using a combination of mathematical

15 pts

13 pts

Die Entwicklung der ersten Hälfte des 20. Jahrhunderts stand unter dem Einfluss von David Hilberts Liste von 23 mathematischen Problemen. Eines der Probleme war der Versuch einer vollständigen Axiomatisierung der Mathematik; gleichzeitig gab es starke Bemühungen

zur Abstraktion, also des Versuches, Objekte auf ihre wesentlichen Eigenschaften zu reduzieren. So entwick-elte Emmy Noether die Grundlagen der modernen Algebra, Felix Hausdorff die allgemeine Topologie als die Untersuchung topologischer Räume, Stefan Banach den

wohl wichtigsten Begriff der Funktionalanalysis, den nach ihm benannten Banachraum. Eine noch höhere Abstraktionsebene, einen gemeinsamen Rahmen für die Betrachtung ähnlich-er Konstruktionen aus verschiedenen Bereichen der Mathematik, schuf

schließlich die Einführung der Kategorientheorie durch Samuel Eilenberg und Saunders Mac Lane.

Source: https://de.wikipe-dia.org/wiki/Mathematics

8 pts

9 pts

Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to pro-pose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its ab-stractness, some emphasize certain topics within mathematics. Today, no consensus on the defini-tion of mathematics prevails, even among profes-sionals. There is not even consensus on whether mathematics is an art or a science.

Aristotle defined mathematics as "the science of quanti-ty", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathe-matics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and meas-urement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.Aristotle defined mathematics as "the science of quantity", and this definition prevailed until the 18th century. Starting in the 19th century, when the study of mathematics increased in rigor and began to address abstract topics such as group theory and projective geometry, which have no clear-cut relation to quantity and measurement, mathematicians and philosophers began to propose a variety of new definitions. Some of these definitions emphasize the deductive character of much of mathematics, some emphasize its abstractness, some emphasize certain topics within mathematics. Today, no consensus on the definition of mathematics prevails, even among professionals. There is not even consensus on whether mathematics is an art or a science.

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